New Quasi Exactly Solvable Difference Equation
arXiv:0712.2616 · doi:10.2991/jnmp.2008.15.s3.36
Abstract
Exact solvability of two typical examples of the discrete quantum mechanics, i.e. the dynamics of the Meixner-Pollaczek and the continuous Hahn polynomials with full parameters, is newly demonstrated both at the Schroedinger and Heisenberg picture levels. A new quasi exactly solvable difference equation is constructed by crossing these two dynamics, that is, the quadratic potential function of the continuous Hahn polynomial is multiplied by the constant phase factor of the Meixner-Pollaczek type. Its ordinary quantum mechanical counterpart, if exists, does not seem to be known.
LaTeX with jnmp class, 12 pages, no figure, submitted for publication in the Proceedings of NEEDS 2007, which will be published as a special issue of Journal of Nonlinear mathematical Physics
References in corpus (10)
- Unified Theory of Annihilation-Creation Operators for Solvable (`Discrete') Quantum Mechanics
- Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
- Shape Invariant Potentials in "Discrete Quantum Mechanics"
- Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
- Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials
- Quasi Exactly Solvable Difference Equations
- Equilibria of `Discrete' Integrable Systems and Deformations of Classical Orthogonal Polynomials
- Multi-Particle Quasi Exactly Solvable Difference Equations
- Equilibrium Positions and Eigenfunctions of Shape Invariant (`Discrete') Quantum Mechanics
- Exact Heisenberg operator solutions for multi-particle quantum mechanics
Cited by in corpus (9)
- Exactly Solvable Quantum Mechanics and Infinite Families of Multi-indexed Orthogonal Polynomials
- Exactly solvable `discrete' quantum mechanics; shape invariance, Heisenberg solutions, annihilation-creation operators and coherent states
- Discrete Quantum Mechanics
- Orthogonal Polynomials from Hermitian Matrices II
- Unified theory of exactly and quasi-exactly solvable `Discrete' quantum mechanics: I. Formalism
- Bethe Ansatz Solutions to Quasi Exactly Solvable Difference Equations
- Exactly and quasi-exactly solvable `discrete' quantum mechanics
- Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model
- Computational solution to quantum foundational problems